How Can I Use Dynamic Sky from a Python script?
I'd recommend enable Developer Extras in the Preferences to get the actual operator (button) call. Once enabled, this is going to add a new Edit Source entry to the RMB context menu which allows to inspect the associated code coming from the the add-on in the Text Editor:
 

Turns out to be a pretty simple add-on, just creates a certain world node tree and allows to control its contents using a panel. The code itself consists of only one sky.dyn() operator, one scene property Scene.dynamic_sky_name storing the name of the current data-block and the panel of course.
Proof using the python console on how to create a 'Dynamic Sky', get the reference, assign it to the world data-block and set the brightness to 2:
# Call the operator
&gt;&gt;&gt; bpy.ops.sky.dyn()
{'FINISHED'}

# Get the created world data block
&gt;&gt;&gt; dyn_sky = D.worlds.get(C.scene.dynamic_sky_name)
&gt;&gt;&gt; dyn_sky
bpy.data.worlds['Dynamic_1']

# Assign the data-block to scene world
&gt;&gt;&gt; C.scene.world = dyn_sky

# Get the Scene_Brightness node 
&gt;&gt;&gt; scene_brightness = C.scene.world.node_tree.nodes.get(&quot;Scene_Brightness&quot;)
&gt;&gt;&gt; scene_brightness
bpy.data.worlds['Dynamic_2'].node_tree.nodes[&quot;Scene_Brightness&quot;]

# Set the strength to 2
&gt;&gt;&gt; scene_brightness.inputs['Strength'].default_value = 2


How to enable a certain add-on is nicely explained in the following Q&amp;A:
How to enable and disable Add-ons via Python?